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Counting and characterising functions with “fast points” for differential attacks

Content Provider	Springer Nature Link
Author	Sălăgean, Ana Mandache Sălăgean, Matei
Copyright Year	2015
Abstract	Higher order derivatives have been introduced by Lai in a cryptographic context. A number of attacks such as differential cryptanalysis, the cube and the AIDA attack have been reformulated using higher order derivatives. Duan and Lai have introduced the notion of “fast points” of a polynomial function f as being vectors a so that computing the derivative with respect to a decreases the total degree of f by more than one. This notion is motivated by the fact that most of the attacks become more efficient if they use fast points. Duan and Lai gave a characterisation of fast points and Duan et al. gave some results regarding the number of functions with fast points in some particular cases. We firstly give an alternative characterisation of fast points and secondly give an explicit formula for the number of functions with fast points for any given degree and number of variables, thus covering all the cases left open in Duan et al. Our main tool is an invertible linear change of coordinates which transforms the higher order derivative with respect to an arbitrary set of linearly independent vectors into the higher order derivative with respect to a set of vectors in the canonical basis. Finally we discuss the cryptographic significance of our results.
Starting Page	217
Ending Page	239
Page Count	23
File Format	PDF
ISSN	19362447
Journal	Cryptography and Communications
Volume Number	9
Issue Number	2
e-ISSN	19362455
Language	English
Publisher	Springer US
Publisher Date	2015-11-26
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Higher order differential attacks Higher order derivative Cryptanalysis Polynomials over finite fields Cryptography Arithmetic theory of polynomial rings over finite fields Data Structures, Cryptology and Information Theory Coding and Information Theory Communications Engineering, Networks Information and Communication, Circuits Mathematics of Computing
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Networks and Communications Computational Theory and Mathematics

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